# Stored data for newform 825.4.a.v, downloaded from the LMFDB on 20 April 2024.
{"label": "825.4.a.v", "space_label": "825.4.a", "level": 825, "weight": 4, "hecke_orbit": 22, "hecke_orbit_code": 94575592241890105, "dim": 4, "is_polredabs": true, "nf_label": "4.4.91035289.2", "trace_hash": 639645274855550215, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-4, -1, 1]], [7, [303074, 7047, -1127, -11, 1]]], "qexp_display": "q-\\beta _{3}q^{2}-3q^{3}+(-4-\\beta _{3})q^{4}+3\\beta _{3}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 13200, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 48.67657575473601, "hecke_ring_index": 4, "level_radical": 165, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 1, [551, 727, 376], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 91035289, "field_disc_factorization": [[17, 2], [19, 1], [59, 1], [281, 1]], "field_poly": [19616, 286, -285, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "3.740", "prec": 17}, {"__RealLiteral__": 0, "data": "0.081", "prec": 17}, {"__RealLiteral__": 0, "data": "36.715", "prec": 20}, {"__RealLiteral__": 0, "data": "1.930", "prec": 17}, {"__RealLiteral__": 0, "data": "540.455", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, 1], [11, 1]], "trace_display": [2, -12, 0, 11], "traces": [0, 4, 2, -12, -14, 0, -6, 11, -6, 36, 0, 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